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Additional info for Applications of Number Theory to Numerical Analysis

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COEFFICIENTS A Method of Korobov The second set of calculations to be reported in this paper were based on the following theorem of Korobov [2, p. 148]: For any s, if N^9N^,... is the sequence of prime numbers, there is a sequence of 2 integerss-1 α Ί ,α ? ,... p. sequence. One way to construct such a se- quence of α·'s is to set a. % equal to that a which minimizes ? ,α ),2). ) This can be done directly for any Ν (not necessarily prime) by calculating N-l. for all α between 1 and I shall denote the minimum value obtained by and any minimizing α by α (Ν,s).

The values found for BN log J N and indicate that Β may have been rather close to Comparison with the tenth line of Table III shows that was less that 1/3 the error bound of the corresponding formula (same s and N) found by the third method. I hope to report on further experiments with this approach in the near future. I wish to thank Miss Susan L. Zuckerman of New College, Sarasota, Florida, and Mr. David Sookne of the National Bureau of Standards for their aid in programming the calculations reported in this paper.